1. Field of the Invention
The present invention relates to a method for generating optimal pulses for magnetic resonance imaging using spatial modulation of magnetization (SPAMM), and more particularly, to a method for specifying the desired magnetization in certain frequency ranges and the desired smoothness for each range and then using the specified values to generate a pulse sequence which will optimally achieve the desired magnetization and smoothness for imaging.
2. Description of the Prior Art
Nuclear magnetic resonance (NMR) has many applications in chemistry and biology. Recent advances have made it possible to use NMR to image the human body. Because much of the body is water, which gives an excellent NMR signal, NMR can yield detailed images of the body and information about various disease processes.
The physical basis of NMR is that many nuclei, such as protons, have a magnetic spin. When an external field, B.sub.0 (in the z axis direction), is applied to a system whose elements have a magnetic spin, the individual elements of the system precess around B.sub.0 according to the Larmor frequency. The Larmor frequency, for typical values of the external field B.sub.0 and for typical nuclei being investigated, is in the radio frequency (rf) range.
Generally, in NMR the system is perturbed by an alternating signal having a frequency .omega. at or near the Larmor frequency of the spins of interest, whose magnetic field (B.sub.1) is normal to B.sub.0. This field is called a pulse. Any spin with a Larmor frequency close to .omega. will interact with the applied field and rotate away from the z axis towards the xy plane. This interaction is called excitation of the spins. The precise axis of rotation and amount of rotation depend on the strength of the pulse, the duration of the pulse, and the difference between .omega. and .omega..sub.0. If B.sub.1 is very strong in relation to the off-resonance effects (.omega.-.omega..sub.0), then the rotation will be essentially around an axis in the xy plane and is called a hard pulse. Generally, the stronger the B.sub.1 field, the broader range of frequencies that it will perturb. The longer the B.sub.1 field is on, and the stronger the B.sub.1 field is, the more the spins will be perturbed.
In a typical application, the spins of interest will have different .omega..sub.0 values, either because they have a different environment, or because B.sub.0 varies with location (a gradient). Furthermore, one needs to have different types of excitation of the spins depending on the application. The three most commonly needed types of excitation are described as a .pi./2 pulse, which rotates spins from the z axis to the xy plane, a .pi. pulse, which rotates spins from pointing in the positive z direction towards the negative z direction, and a refocusing pulse, which rotates spins of interest 180.degree. about an axis in the xy plane, the axis being the same for all spins of interest. However, other types of excitation profiles can be needed, and one may need to apply a different type of excitation to different frequencies.
NMR imaging schemes depend on applying magnetic field gradients so that different nuclei at different locations experience different magnetic fields and, therefore, have different frequencies. Accordingly, the location of the nucleus determines its frequency. One then applies a pulse, which rotates, or excites, the nuclei, and therefore, the magnetic dipole moment. One tries to excite only nuclei which have frequencies corresponding to the slice of tissue which it is desired to image, and to excite those nuclei to the same degree.
Thus, it is necessary to design pulses which perturb a particular range of frequencies to the same extent but that do not perturb all other frequencies. This "ideal" pulse is physically unrealizable. However, it has been possible to generate pulses which will do this more or less perfectly. As a result, much work in the NMR imaging art has gone into generating pulses which will give very "sharp" slices, for the sharper the slice, the better the resolution of the image.
Previously, so-called "hard" radio frequency pulses have been used to give sharp slices for imaging. As known by those skilled in the art, a "hard" pulse is a constant amplitude rectangular radio frequency pulse in which the strength of the applied alternating field is sufficiently large that the pulse can be assumed to affect all frequencies of interest equally. Selective excitation is thus achieved by applying several pulses in a row and varying pulse widths and inter-pulse delay times. Different frequencies precess for different amounts during the delays between the pulses and thus respond differently to the pulse sequence. Many pulse sequences using hard pulses have been devised for different applications in NMR imaging, as described by P. J. Hore in an article entitled "Solvent Suppression in Fourier Transform Nuclear Magnetic Resonance", Journal of Magnetic Resonance, Vol. 55, pp. 283-300 (1983), for example, and by Brandes in U.S. Pat. No. 4,695,798.
However, hard pulse sequences have several major limitations. First the frequency response of hard pulses have "side lobes" or harmonics around the desired frequency range. The location of the side lobes depends on the delay between pulses. Second, if the frequency range of interest is large, as it is in NMR imaging, it may be difficult to create pulses that are strong enough to be considered "hard". Furthermore, the frequency response of hard pulse sequences currently in use is far from ideal.
Despite these limitations, hard pulses have been used effectively in the technique called spatial modulation of magnetization (SPAMM) described in the afore-mentioned parent application to image the heart wall. As described therein, SPAMM has been used to simultaneously create parallel sheets of altered magnetization that show up as stripes in subsequent images. Motion of the "tagged" tissue between the times of SPAMM application and imaging results in a corresponding displacement of the stripes, thereby permitting study of motions. Nevertheless, continuing efforts have been made to find pulse sequences with the desired frequency response and amplitude such that the best possible imaging stripes can be used.
For example, in an article entitled "Heart Wall Motion: Improved Method of Spatial Modulation of Magnetization for MR Imaging", Radiology, Vol. 172, August 1989, pp. 349-350, one of the present inventors implements SPAMM using a binomial series of radio frequency pulses which are separated by equal gradient pulses. In this sequence, during the radio frequency pulses all spins are on resonance, so the pulses are "hard", i.e., their effect on the spins is independent of the spatial location. The frequency encoding then occurs during the gradient pulses. The result is a sequence of hard pulses with free precession between the pulses. Because of the nice stripes generated when such binomial pulses were used, binomial pulses have been preferred for use with SPAMM. However, binomial pulse sequences provide limited flexibility because the relationships of the amplitudes of the binomial pulses are predefined and cannot be adjusted by the SPAMM user.
Others have also expended considerable effort in devising pulses which have better frequency characteristics. One of the best of these is the hyperbolic secant pulse described by M. S. Silver et al. in an article entitled "Highly Selective .pi./2 and .pi. Pulse Generation", Journal of Magnetic Resonance, Vol. 59, pp. 347-351 (1984). Unfortunately, even the response to this pulse does not have an ideal frequency response. Moreover, implementation of this pulse requires a spectrometer which can simultaneously modulate the amplitude and phase of the applied external field, which many spectrometers cannot do. Indeed, patents have issued on the instrumentation for the delivery of certain shaped pulses to the transmitter, such as the afore-mentioned patent to Brandes. Further continuing efforts to devise improved pulses are described by, for example, H. Yan and J. Gore in an article entitled "Improved Selective 180.degree. Radio Frequency Pulses for Magnetization Inversion and Phase Reversal", Journal of Magnetic Resonance, Vol. 71, pp. 116-131 (1987). However, such other techniques of pulse generation for MR imaging do not provide selective pulses that have periodic excitations needed for creating the selective stripes of SPAMM, and, in any event, such pulse sequences are generally too long to be used with SPAMM. Better pulses for use with SPAMM are thus not suggested in the prior art.
In addition, the frequency response of a general system such as SPAMM has been studied by one of the present inventors in a sequence of papers: S. M. Eleff et al., "The Synthesis of Pulse Sequences Yielding Arbitrary Symmetric Magnetization Vectors" Journal of Magnetic Resonance, Vol. 12, pp 291-306 (1987); M. Shinnar and J. S. Leigh, "Frequency Response of Soft Pulses", Journal of Magnetic Resonance, Vol. 75, pp. 502-505 (1987); M. Shinnar and J. S. Leigh, "The Application of Spinors to Pulse Synthesis and Analysis", Journal of Magnetic Resonance in Medicine, Vol. 12, pp. 93-98 (1989); M. Shinnar et al., "The Use Of Finite Impulse Response Filters in Pulse Design", Journal of Magnetic Resonance in Medicine, Vol. 12, pp. 81-87 (1989); M. Shinnar et al., "The Synthesis of Pulse Sequences Yielding Arbitrary Magnetization Vectors", in Journal of Magnetic Resonance in Medicine, Vol. 12, pp. 74-80 ( 1989); and M. Shinnar et al., "The Synthesis of Soft Pulses With a Specified Frequency Response", Journal of Magnetic Resonance in Medicine, Vol. 12, pp. 88-92 (1989).
It was therein shown that the frequency response of a series of pulses can be written as a Fourier series, whose coefficients are nonlinear functions of the pulse amplitudes. A method was also described whereby, if one specified the desired M.sub.z magnetization as a Fourier series, one could generate a pulse sequence which will actually yield that magnetization. Furthermore, the way of specifying the desired M, magnetization as a Fourier series was realized to be identical to a solved problem in the design of finite impulse response filters. Using this technique, which has been described in detail in the afore-mentioned co-pending U.S. patent application Ser. No. 07/655,077, (now U.S. Pat. No. 5,153,155) one could specify the desired magnetization in certain frequency ranges, the desired smoothness for each range, and then generate a pulse sequence which would optimally achieve that desired magnetization.
The present inventors then joined forces to investigate whether the afore-mentioned pulse generation technique could be applied to the design of a pulse sequence or sequences which would be better than the afore-mentioned binomial sequence for SPAMM imaging. Since the stripes laid down for the SPAMM technique correspond to setting the z magnetization M.sub.z, in certain frequency ranges, it seemed ideally suited for this pulse generation technique. As will be described herein, the present inventors have in fact found that improved images can be produced by using pulses generated in accordance with the afore-mentioned pulse generation technique in place of binomial pulses. The present invention is thus believed to meet the long-felt needs of the prior art.